Problem: Michael is 12 years older than Jessica. Two years ago, Michael was 3 times as old as Jessica. How old is Jessica now?
Explanation: We can use the given information to write down two equations that describe the ages of Michael and Jessica. Let Michael's current age be $m$ and Jessica's current age be $j$ The information in the first sentence can be expressed in the following equation: $m = j + 12$ Two years ago, Michael was $m - 2$ years old, and Jessica was $j - 2$ years old. The information in the second sentence can be expressed in the following equation: $m - 2 = 3(j - 2)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $j$ , it might be easiest to use our first equation for $m$ and substitute it into our second equation. Our first equation is: $m = j + 12$ . Substituting this into our second equation, we get the equation: $(j + 12)$ $-$ $2 = 3(j - 2)$ which combines the information about $j$ from both of our original equations. Simplifying both sides of this equation, we get: $j + 10 = 3 j - 6$ Solving for $j$ , we get: $2 j = 16$ $j = 8$.